What is the Greatest Common Factor of 27648 and 27666?

Greatest common factor (GCF) of 27648 and 27666 is 18.

GCF(27648,27666) = 18

We will now calculate the prime factors of 27648 and 27666, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27648 and 27666.

How to find the GCF of 27648 and 27666?

We will first find the prime factorization of 27648 and 27666. After we will calculate the factors of 27648 and 27666 and find the biggest common factor number .

Step-1: Prime Factorization of 27648

Prime factors of 27648 are 2, 3. Prime factorization of 27648 in exponential form is:

27648 = 2¹⁰ × 3³

Step-2: Prime Factorization of 27666

Prime factors of 27666 are 2, 3, 29, 53. Prime factorization of 27666 in exponential form is:

27666 = 2¹ × 3² × 29¹ × 53¹

Step-3: Factors of 27648

List of positive integer factors of 27648 that divides 27648 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1024, 1152, 1536, 1728, 2304, 3072, 3456, 4608, 6912, 9216, 13824

Step-4: Factors of 27666

List of positive integer factors of 27666 that divides 27648 without a remainder.

1, 2, 3, 6, 9, 18, 29, 53, 58, 87, 106, 159, 174, 261, 318, 477, 522, 954, 1537, 3074, 4611, 9222, 13833

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27648 and 27666. The biggest common factor number is the GCF number.
So the greatest common factor 27648 and 27666 is 18.

Also check out the Least Common Multiple of 27648 and 27666